| Summary: | Since the notion of <i>T</i>-equivalence, where <i>T</i> is a t-norm, was introduced as a fuzzy generalization of the notion of crisp equivalence relation, many researchers have worked in the study of the metric behavior of such fuzzy relations. Concretely, a few techniques to induce metrics from <i>T</i>-equivalences, and vice versa, have been developed. In several fields of computer science and artificial intelligence, a generalization of pseudo-metric, known as partial pseudo-metrics, have shown to be useful. Recently, Bukatin, Kopperman and Matthews have stated that the notion of partial pseudo-metric and a type of generalized <i>T</i>-equivalence are linked. Inspired by the preceding fact, in this paper, we state a concrete relationship between partial pseudo-metrics and the aforesaid generalized <i>T</i>-equivalences. Specifically, a method for constructing partial pseudo-metrics from the new type of <i>T</i>-equivalences and, reciprocally, for constructing the generalized <i>T</i>-equivalences from partial pseudo-metrics are provided. However, important differences between the new approach and the classical one are established. Special interest is paid to the case in which the minimum, drastic, and Łukasiewicz t-norms are under consideration.
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